Proton cancer therapy (PCT) uses high-energy protons to kill cancerous tumors with minimum damage on healthy tissues and without the side effects of X-ray therapy. Colliding protons induce cell water radiolysis reactions that generate reactive species: ions, electrons and radicals. Those species damage the DNA of cancerous cells, prompting their apoptosis. Despite established clinical use, the microscopic details of PCT reactions remain elusive. That has prevented a rational design of PCT that can maximize its therapeutic power and minimize its side effects. This poor characterization of PCT is due to the fact that even the most advanced experimental/clinical techniques cannot completely reveal the microscopic details of PCT, especially without harming human subjects. To overcome this situation, we are conducting computer simulations of PCT reactions with novel quantum-dynamics methods. Thus, dangerous PCT reactions that cannot be safely tested in the human body are innocuously run on computers at a very low cost. Our proposed quantum-dynamics methods are based on the electron nuclear dynamics (END) theory ?a time-dependent, variational, on-the-fly and non- adiabatic method? implemented in our parallel code PACE. We will study three main types of PCT reactions: (1) PCT water radiolysis reactions?the fundamental PCT reactions in cell water that produce the ions, electrons and radicals that damage cellular DNA; (2) proton-induced DNA damage and (3) electron-induced DNA damage. For (3), we will verify Simons' mechanism for electron-induced DNA damage (electron capture in a DNA base, transfer through sugar, and single strand break at the phospho-ester bond) and other competing mechanisms revealed by recent DNA experiments. We are the first performing time-dependent, non-adiabatic simulations of large nucleotide samples for reactions (2) and (3). Our studies will provide results not obtained before by other computer simulations and experiments, such as the precise determination of the mechanisms of PCT reactions and the accurate prediction of reactions integral cross sections. Those cross sections are the needed input data to design Monte Carlo (MC) codes used for radiation dosimetry, radiotherapy sessions, radioprotection protocols and medical imaging (the team of the MC code TILDA-V has paid attention to some of our results in their designs). Thus, our studies are making a positive impact on PCT research and therapeutics and on other areas of ion- induced DNA damage research such as non-cancerous radiotherapy, studies of mutagenesis, ageing, etc. We will use both existing and new END methods. Existing methods are the simplest-level END and our END/Kohn- Sham Density Functional Theory that includes electron correlation effects. Both methods adopt nuclear classical mechanics and an electronic single-determinantal wavefunction. New methods to be developed with this grant are END with the continuum polarizable model, to describe the solvation effects on PCT reactions by cell bulk water, and END with plane waves, to accurately describe scattering/capture of unbound electrons from water/to DNA. With these new methods, PACE will become a more accurate and versatile tool to describe PCT processes.